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Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans

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Abstract

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This paper develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in an accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. The result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.

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Acknowledgments

This work was supported by the National Natural Science Foundation (Nos. 41201420, 41130744), Beijing Nova Program (No. Z111106054511097) and Beijing Young Talent Program. We benefited from discussions with Robert W. Ritzi of the Wright State University and his comments and suggestions greatly improve this paper.

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Authors and Affiliations

  1. College of Resources Environment and Tourism, Capital Normal University, Laboratory Cultivation Base of Environment Process and Digital Simulation, Beijing, 100048, China

    Lin Zhu & Huili Gong

  2. Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Lin Zhu, Zhenxue Dai & Carl Gable

  3. Department of Civil, Environmental and Architectural Engineering, University of Padova, Padua, Italy

    Pietro Teatini

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  1. Lin Zhu
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  2. Zhenxue Dai
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  3. Huili Gong
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  4. Carl Gable
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  5. Pietro Teatini
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Correspondence to Zhenxue Dai or Huili Gong.

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Zhu, L., Dai, Z., Gong, H. et al. Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans. Stoch Environ Res Risk Assess 30, 1005–1016 (2016). https://doi.org/10.1007/s00477-015-1089-2

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